Find a degree 3 polynomial having zeros -6, 6 and 0 and leading coefficient equal to 1

amanf

amanf

Answered question

2021-07-01

Find a degree 3 polynomial having zeros -6, 6 and 0 and leading coefficient equal to 1

Answer & Explanation

Jaylen Fountain

Jaylen Fountain

Skilled2021-07-03Added 169 answers

Here is video solution

Ian Adams

Ian Adams

Skilled2021-08-04Added 163 answers

If c is a zero of a polynomial, then x−c is a linear factor of this polynomial.
Given the zeros −6, 6, and 0, we can write:
f(x)=a(x+6)(x6)(x)
Expand:
f(x)=a(x236)(x)
f(x)=a(x336x) Since the leading coefficient is equal to 1, we simply let a=1:
f(x)=1(x336x)
f(x)=x336x

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